The offer of 840 pence per share represents a premium of 36.6 percent to BTG's close of 615 pence on Monday.
Shares of BTG soared more than 35 percent to 832 pence, their highest level since Jan. 2015, on Tuesday. Up to Monday's close, the stock had slipped 19.3 percent this year.
Boston Scientific said BTG's interventional portfolio — using devices to deliver drugs to affected organs — would augment its capabilities in important areas of unmet need such as cancer and pulmonary embolism.
BTG, which has long produced drugs to treat overdoses and rattlesnake bites, has focused on interventional medicine in recent years, for example producing beads that target tumors.
Boston Scientific's chairman and CEO Michael F. Mahoney said the addition of these therapies to our portfolio would ultimately advance patient care in ways that could not be realised by either company alone, while also providing a strong return for investors.
BTG said it considered the terms of the offer to be fair and reasonable and it planned to recommend the deal to shareholders.